How effective is carnitine in helping you get some weight loss?

Depends. Liquid carnitine seems to be effective but it depends on the type of diet you are on. It requires a very low carbohydrate intake, not a balanced approach and requires exercise while taking it. I don't advise any diet or supplements without first talking to your doctor to be sure it is right and safe for you and will be helpful on learning habits to keep the weight off long term.
Improves weight loss. Study done - one group was given 2000 mg of carnitine, and the other a placebo. In the placebo group, the average weight loss after 12 weeks was one pound. In the carnitine group, weight loss averaged 11 pounds. That’s an eleven-fold increase in weight loss, simply by increasing carnitine levels.